Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
"""Ввод размера матрицы"""
nm = [int(s) for s in input().split()]

"""Ввод массива"""
a = []
for i in range(nm[0]):
    a.append([int(j) for j in input().split()])

rez=[]

def stroka():
    global rez
    rez_row=[]
    rez_r=0
    for i in range(nm[0]):
        min_row=501
        for j in range(nm[1]):
            if a[i][j]< min_row:
                min_row=a[i][j]
        rez_r+=min_row

        if min_row != 0:
            for c in range(min_row):
                rez.append('row ' + str(i+1))

        for j in range(nm[1]):
            if a[i][j]>0:
                a[i][j]-= min_row

def grafa():
    global rez
    rez_c=0
    for j in range(nm[1]):
            min_col=501
            for i in range(nm[0]):
                if a[i][j]< min_col:
                    min_col=a[i][j]
            rez_c+=min_col

            if min_col !=0:
                for c in range(min_col):
                    rez.append('col '+ str(j+1))
            for i in range(nm[0]):
                if a[i][j]>0:
                    a[i][j] -=min_col


if nm[0]<nm[1]:
    stroka()
    grafa()
else:
    grafa()
    stroka()

maxEl = max(max(a))

if maxEl == 0:
    print(len(rez))
    for el in rez:
        print(el)
else:
    print(-1)